Question

An electromagnetic wave is travelling in vertically upward direction. At an instant, its electric field vector points in west direction. In which direction does the magnetic field vector point at that instant?

Hint:

The direction of the magnetic field in an electromagnetic wave is determined by the right-hand rule, which ensures it is perpendicular to both the electric field and the direction of propagation.

Answer 1

We are given an electromagnetic wave traveling in the vertically upward direction, and at a certain instant, its electric field vector points in the west direction. We are tasked with determining the direction of the magnetic field vector at that instant.

1. Understanding the Relationship Between Electric and Magnetic Fields in an Electromagnetic Wave:

In an electromagnetic wave, the electric field (\( \vec{E} \)) and magnetic field (\( \vec{B} \)) are always perpendicular to each other and also perpendicular to the direction of propagation of the wave. This means the three vectors—electric field, magnetic field, and the direction of wave propagation—form a right-handed coordinate system.

2. Direction of Propagation and Fields:

Let's define the directions using a coordinate system:

• The wave is traveling in the vertically upward direction, which corresponds to the \( +y \)-axis in a typical 3D coordinate system.
• The electric field vector (\( \vec{E} \)) points in the west direction, which corresponds to the \( -x \)-axis (since west is usually defined as negative \( x \)-direction in a standard geographic coordinate system).
• According to the right-hand rule, the magnetic field (\( \vec{B} \)) must be perpendicular to both the electric field vector (\( \vec{E} \)) and the direction of propagation of the wave (the \( y \)-axis).

3. Applying the Right-Hand Rule:

To find the direction of the magnetic field vector (\( \vec{B} \)), we use the right-hand rule, which states that if the thumb of your right hand points in the direction of wave propagation (upward, or \( +y \)-axis), and the index finger points in the direction of the electric field (\( -x \)-axis, or west), then the middle finger will point in the direction of the magnetic field.

Using the right-hand rule, with the electric field pointing west (along \( -x \)) and the wave propagating vertically upward (along \( +y \)), the magnetic field vector will point in the north direction, or along the \( +z \)-axis.

4. Conclusion:

At the instant when the electric field vector points in the west direction, the magnetic field vector points in the north direction.